Generally, flooded lead-acid batteries are the most popular for off-grid systems. This is because they are widely available, cheap, and there are many systems that support the tech. For a good example, check out the Outback SystemEdge series for a few different turn-key options.
It can be expected that lithium-ion battery systems will soon take this spot for longevity and performance, but the cost is still a bit prohibitive for most. One example of an up and coming system is the Darfon H302. This is an affordable system that can be utilized for off-grid systems if necessary.
See a comparison of the Darfon vs Outback vs SolarEdge Battery Backup Systems